Search NASA⌕ Search

SEARCH · Search NASA

Results for “Optimal Control Problem”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A memory-distributed quasi-Newton solver for nonlinear programming problems with a small number of general constraints

We approach the problem of parallelizing state-of-the-art nonlinear programming optimization algorithms.Specifically, we focus on parallelizing quasi-Newton interior-point methods that use limited-memory secant Hessian approximations. Such interior-point methods are known to have better convergence properties and to be more effective on large-scale problems than gradient-based and derivative-free optimization algorithms. We target nonlinear and potentially nonconvex optimization problems with an arbitrary number of bound constraints and a small number of general equality and inequality constraints on the optimization variables. These problems occur for example in the form of optimal control, optimal design, and inverse problems governed by ordinary or partial differential equations, whenever they are expressed in a “reduced-space” optimization approach. We introduce and analyze the time and space complexity of a decomposition method for solving the quasi-Newton linear systems that leverages the fact that the quasi-Newton Hessian matrix has a small number of dense blocks that border a low-rank update of a diagonal matrix. This enables an efficient parallelization on memory-distributed computers of the iterations of the optimization algorithm, a state-of-the-art filter line-search interior-point algorithm by Wächter et. al. We illustrate the efficiency of the proposed method by solving structural topology optimization problems on up to 4608 cores on a parallel machine.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1979

Formulations and applications of large structure actuator and sensor placements

A new approach based on the steady-state solutions of the optimal control and estimation problems is presented to study respectively the actuator and sensor locations for large flexible structures. A simple and computer-implementable formulation for minimizing the steady state optimal cost function and the state estimation error inherent in the estimation process is given. In conjunction with the new approach, two criteria are established relating the actuator and the sensor placement optimalities respectively to the minimums of the optimal cost function and the state estimation error. To illustrate the concepts of this paper, we present the results of some numerical and analytical studies on the actuator and the sensor locations of several simple flexible beam modes.

Juang, J.-N.↗
NASA NTRS2008

Robust Path Planning and Feedback Design Under Stochastic Uncertainty

Autonomous vehicles require optimal path planning algorithms to achieve mission goals while avoiding obstacles and being robust to uncertainties. The uncertainties arise from exogenous disturbances, modeling errors, and sensor noise, which can be characterized via stochastic models. Previous work defined a notion of robustness in a stochastic setting by using the concept of chance constraints. This requires that mission constraint violation can occur with a probability less than a prescribed value.In this paper we describe a novel method for optimal chance constrained path planning with feedback design. The approach optimizes both the reference trajectory to be followed and the feedback controller used to reject uncertainty. Our method extends recent results in constrained control synthesis based on convex optimization to solve control problems with nonconvex constraints. This extension is essential for path planning problems, which inherently have nonconvex obstacle avoidance constraints. Unlike previous approaches to chance constrained path planning, the new approach optimizes the feedback gain as wellas the reference trajectory.The key idea is to couple a fast, nonconvex solver that does not take into account uncertainty, with existing robust approaches that apply only to convex feasible regions. By alternating between robust and nonrobust solutions, the new algorithm guarantees convergence to a global optimum. We apply the new method to an unmanned aircraft and show simulation results that demonstrate the efficacy of the approach.

autonomuys vehicles↗
NASA NTRS1989

Optimal guidance and propulsion control for transatmospheric vehicles

Problems associated with on-board trajectory optimization and with the synthesis of guidance laws are addressed for ascent to LEO of an air-breathing, single-stage-to-orbit vehicle. A multimode propulsion system is assumed which incorporates turbojet, ramjet, scramjet, and rocket engines. An energy-state approximation is applied to a four-state dynamic model for flight of a point mass over a spherical nonrotating earth. An algorithm for generating fuel-optimal climb profiles is derived via singular perturbation theory. This algorithm results from application of the minimum principle to a low-order dynamic model that includes general functional dependence on angle of attack and a normal component of thrust. Switching conditions are derived which, under appropriate assumptions, govern optimal transition from one propulsion mode to another. The use of bank angle to modulate the magnitude of the vertical component of lift is shown to improve the index performance. Numerical results illustrate the nature of the resulting fuel-optimal climb paths.

Corban, J. E.↗
NASA NTRS1989

Analysis of a turning point problem in flight trajectory optimization

The optimal control policy for the aeroglide portion of the minimum fuel, orbital plane change problem for maneuvering entry vehicles is reduced to the solution of a turning point problem for the bank angle control. For this problem a turning point occurs at the minimum altitude of the flight, when the flight path angle equals zero. The turning point separates the bank angle control into two outer solutions that are valid away from the turning point. In a neighborhood of the turning point, where the bank angle changes rapidly, an inner solution is developed and matched with the two outer solutions. An asymptotic analysis of the turning point problem is given, and an analytic example is provided to illustrate the construction of the bank angle control.

Gracey, C.↗
NASA NTRS1995

Optimal Trajectories and Control Strategies for the Helicopter in One-Engine-Inoperative Terminal-Area Operations

Engine failure represents a major safety concern to helicopter operations, especially in the critical flight phases of takeoff and landing from/to small, confined areas. As a result, the JAA and FAA both certificate a transport helicopter as either Category-A or Category-B according to the ability to continue its operations following engine failures. A Category-B helicopter must be able to land safely in the event of one or all engine failures. There is no requirement, however, for continued flight capability. In contrast, Category-A certification, which applies to multi-engine transport helicopters with independent engine systems, requires that they continue the flight with one engine inoperative (OEI). These stringent requirements, while permitting its operations from rooftops and oil rigs and flight to areas where no emergency landing sites are available, restrict the payload of a Category-A transport helicopter to a value safe for continued flight as well as for landing with one engine inoperative. The current certification process involves extensive flight tests, which are potentially dangerous, costly, and time consuming. These tests require the pilot to simulate engine failures at increasingly critical conditions, Flight manuals based on these tests tend to provide very conservative recommendations with regard to maximum takeoff weight or required runway length. There are very few theoretical studies on this subject to identify the fundamental parameters and tradeoff factors involved. Furthermore, a capability for real-time generation of OEI optimal trajectories is very desirable for providing timely cockpit display guidance to assist the pilot in reducing his workload and to increase safety in a consistent and reliable manner. A joint research program involving NASA Ames Research Center, the FAA, and the University of Minnesota is being conducted to determine OEI optimal control strategies and the associated optimal,trajectories for continued takeoff (CTO), rejected takeoff (RTO), balked landing (BL), and continued landing (CL) for a twin engine helicopter in both VTOL and STOL terminal-area operations. This proposed paper will present the problem formulation, the optimal control solution methods, and the key results of the trajectory optimization studies for both STOL and VTOL OEI operations. In addition, new results concerning the recently developed methodology, which enable a real-time generation of optimal OEI trajectories, will be presented in the paper. This new real-time capability was developed to support the second piloted simulator investigation on cockpit displays for Category-A operations being scheduled for the NASA Ames Vertical Motion Simulator in June-August of 1995. The first VMS simulation was conducted in 1994 and reported.

Chen, Robert T. N.↗
DOE OSTI2023

Towards constrained grid-forming control

Grid-forming converters are commonly envisioned to replace conventional synchronous generators as the cornerstone of future power systems. However, compared to synchronous generators, power converters and their power sources (e.g., renewable generation, energy storage) are subject to significant physical constraints (e.g., current limits, modulation limits). Grid-forming controls are commonly designed neglecting these constraints and subsequently augmented with limiters for a subset of constraints. In this work, we propose a systematic approach to constrained grid-forming control of two-level voltage source converters interfacing photovoltaics. We first formulate grid-forming control objectives and constraints of voltage source converters and photovoltaics in a one-step optimal grid-forming control problem. Next, we leverage primal-dual dynamics to obtain a dynamic feedback controller that approximates the solution of the one-step optimal grid-forming control problem. Finally, electromagnetic transient simulations are used to illustrate the results.

Gross, Dominic↗
DOE OSTI2022

Machine Learning with Gradient-Based Optimization of Nuclear Waste Vitrification with Uncertainties and Constraints

Gekko is an optimization suite in Python that solves optimization problems involving mixed-integer, nonlinear, and differential equations. The purpose of this study is to integrate common Machine Learning (ML) algorithms such as Gaussian Process Regression (GPR), support vector regression (SVR), and artificial neural network (ANN) models into Gekko to solve data based optimization problems. Uncertainty quantification (UQ) is used alongside ML for better decision making. These methods include ensemble methods, model-specific methods, conformal predictions, and the delta method. An optimization problem involving nuclear waste vitrification is presented to demonstrate the benefit of ML in this field. ML models are compared against the current partial quadratic mixture (PQM) model in an optimization problem in Gekko. GPR with conformal uncertainty was chosen as the best substitute model as it had a lower mean squared error of 0.0025 compared to 0.018 and more confidently predicted a higher waste loading of 37.5 wt% compared to 34 wt%. The example problem shows that these tools can be used in similar industry settings where easier use and better performance is needed over classical approaches. Future works with these tools include expanding them with other regression models and UQ methods, and exploration into other optimization problems or dynamic control.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1988

A forward method for optimal stochastic nonlinear and adaptive control

A computational approach is taken to solve the optimal nonlinear stochastic control problem. The approach is to systematically solve the stochastic dynamic programming equations forward in time, using a nested stochastic approximation technique. Although computationally intensive, this provides a straightforward numerical solution for this class of problems and provides an alternative to the usual dimensionality problem associated with solving the dynamic programming equations backward in time. It is shown that the cost degrades monotonically as the complexity of the algorithm is reduced. This provides a strategy for suboptimal control with clear performance/computation tradeoffs. A numerical study focusing on a generic optimal stochastic adaptive control example is included to demonstrate the feasibility of the method.

Bayard, David S.↗
NASA NTRS1990

Stabilization and control of distributed systems with time-dependent spatial domains

This paper considers the problem of the stabilization and control of distributed systems with time-dependent spatial domains. The evolution of the spatial domains with time is described by a finite-dimensional system of ordinary differential equations, while the distributed systems are described by first-order or second-order linear evolution equations defined on appropriate Hilbert spaces. First, results pertaining to the existence and uniqueness of solutions of the system equations are presented. Then, various optimal control and stabilization problems are considered. The paper concludes with some examples which illustrate the application of the main results.

Wang, P. K. C.↗
DOE OSTI2022

Unifying Energy-Management Problems for Inverter-Based Power Networks

This paper outlines a suite of energy-management problems for inverter-based power networks from the vantage point of optimal control and (non)linear optimization. The problems are categorized based on timescales dictated by the network dynamics, and organized methodologically based on the problem complexity. A growing body of literature has addressed problems in this domain, albeit, with poorly motivated assumptions and behavioral models that obscure precise device behavior. With a combination of circuit- and control-theoretic lenses, we establish appropriate dynamic models for the networked resources, illustrate how common engineering assumptions arise, uncover how problems are linked, and postulate open challenges.

(non)linear optimization↗
DOE OSTI2020

Coastal Community Resiliency Enhancement Using Marine Hydrokinetic (MHK) Resources and Networked Microgrids

Enormous challenges are inherent in the operation of modern distribution grids. In particular, distribution feeders can be severely compromised under extreme conditions such as large-scale weather events (e.g., hurricanes, floods, and other types of natural disasters). To combat this problem, they turn to local energy support from distributed energy resources, such as solar and wind, marine hydrolinetic (MHK), and other types of energy. In this report, we investigate the actual characteristics of MHK resources to enhance coastal community resiliency. Two typical types of MHK resources (i.e., wave and tidal resources) illustrate the coastal resilience enhancement framework. By identifying their operational characteristics, such as target time-scales and potential power generation variations, we detail a holistic coastal community resiliency enhancement framework that integrates both optimization and control efforts. The optimization problem is formulated to significantly minimize the power outage time at the critical infrastructures in coastal communities by implementing multiple autonomous and dynamic microgrids around MHK resources. Therefore, during severe power outages caused by natural disasters (e.g., floods, hurricanes), the coastal community load profiles can be satisfied using local MHK resources in each microgrid with limited or no power support from upstream power grids.

16 TIDAL AND WAVE POWER↗
NASA NTRS2013

Robust Maneuvering Envelope Estimation Based on Reachability Analysis in an Optimal Control Formulation

This paper discusses an algorithm for estimating the safe maneuvering envelope of damaged aircraft. The algorithm performs a robust reachability analysis through an optimal control formulation while making use of time scale separation and taking into account uncertainties in the aerodynamic derivatives. Starting with an optimal control formulation, the optimization problem can be rewritten as a Hamilton- Jacobi-Bellman equation. This equation can be solved by level set methods. This approach has been applied on an aircraft example involving structural airframe damage. Monte Carlo validation tests have confirmed that this approach is successful in estimating the safe maneuvering envelope for damaged aircraft.

optimal control↗
NASA NTRS1967

Automatic control

Numerical solution of optimal control and programming problems

FEEDBACK CONTROL SYSTEM↗
NASA NTRS1991

A mathematical basis for the design optimization of adaptive trusses in precision control

Optimal actuator placement schemes are presently studied for cases of adaptive truss precision control and prestressing control, with a view to the maximization of actuator efficiencies. In statically indeterminate truss structures, the optimal placement criteria and techniques differ, depending on whether the primary determinate structure is known. A suboptimal actuator-placement solution to the global optimization problem which combines displacement control and prestressing control is suggested, by combining the separate displacement control and prestressing control optimization results. Attention is given to the results obtained for the illustrative case of a two-bay, three-dimensional precision truss structure.

Das, S. K.↗